[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
|
---|
| 2 | // for linear algebra.
|
---|
| 3 | //
|
---|
| 4 | // Copyright (C) 2009, 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
|
---|
| 5 | // Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net>
|
---|
| 6 | //
|
---|
| 7 | // This Source Code Form is subject to the terms of the Mozilla
|
---|
| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
|
---|
| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
---|
| 10 |
|
---|
| 11 | #ifndef EIGEN_MATRIX_EXPONENTIAL
|
---|
| 12 | #define EIGEN_MATRIX_EXPONENTIAL
|
---|
| 13 |
|
---|
| 14 | #include "StemFunction.h"
|
---|
| 15 |
|
---|
| 16 | namespace Eigen {
|
---|
| 17 |
|
---|
| 18 | /** \ingroup MatrixFunctions_Module
|
---|
| 19 | * \brief Class for computing the matrix exponential.
|
---|
| 20 | * \tparam MatrixType type of the argument of the exponential,
|
---|
| 21 | * expected to be an instantiation of the Matrix class template.
|
---|
| 22 | */
|
---|
| 23 | template <typename MatrixType>
|
---|
| 24 | class MatrixExponential {
|
---|
| 25 |
|
---|
| 26 | public:
|
---|
| 27 |
|
---|
| 28 | /** \brief Constructor.
|
---|
| 29 | *
|
---|
| 30 | * The class stores a reference to \p M, so it should not be
|
---|
| 31 | * changed (or destroyed) before compute() is called.
|
---|
| 32 | *
|
---|
| 33 | * \param[in] M matrix whose exponential is to be computed.
|
---|
| 34 | */
|
---|
| 35 | MatrixExponential(const MatrixType &M);
|
---|
| 36 |
|
---|
| 37 | /** \brief Computes the matrix exponential.
|
---|
| 38 | *
|
---|
| 39 | * \param[out] result the matrix exponential of \p M in the constructor.
|
---|
| 40 | */
|
---|
| 41 | template <typename ResultType>
|
---|
| 42 | void compute(ResultType &result);
|
---|
| 43 |
|
---|
| 44 | private:
|
---|
| 45 |
|
---|
| 46 | // Prevent copying
|
---|
| 47 | MatrixExponential(const MatrixExponential&);
|
---|
| 48 | MatrixExponential& operator=(const MatrixExponential&);
|
---|
| 49 |
|
---|
| 50 | /** \brief Compute the (3,3)-Padé approximant to the exponential.
|
---|
| 51 | *
|
---|
| 52 | * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
|
---|
| 53 | * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
|
---|
| 54 | *
|
---|
| 55 | * \param[in] A Argument of matrix exponential
|
---|
| 56 | */
|
---|
| 57 | void pade3(const MatrixType &A);
|
---|
| 58 |
|
---|
| 59 | /** \brief Compute the (5,5)-Padé approximant to the exponential.
|
---|
| 60 | *
|
---|
| 61 | * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
|
---|
| 62 | * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
|
---|
| 63 | *
|
---|
| 64 | * \param[in] A Argument of matrix exponential
|
---|
| 65 | */
|
---|
| 66 | void pade5(const MatrixType &A);
|
---|
| 67 |
|
---|
| 68 | /** \brief Compute the (7,7)-Padé approximant to the exponential.
|
---|
| 69 | *
|
---|
| 70 | * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
|
---|
| 71 | * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
|
---|
| 72 | *
|
---|
| 73 | * \param[in] A Argument of matrix exponential
|
---|
| 74 | */
|
---|
| 75 | void pade7(const MatrixType &A);
|
---|
| 76 |
|
---|
| 77 | /** \brief Compute the (9,9)-Padé approximant to the exponential.
|
---|
| 78 | *
|
---|
| 79 | * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
|
---|
| 80 | * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
|
---|
| 81 | *
|
---|
| 82 | * \param[in] A Argument of matrix exponential
|
---|
| 83 | */
|
---|
| 84 | void pade9(const MatrixType &A);
|
---|
| 85 |
|
---|
| 86 | /** \brief Compute the (13,13)-Padé approximant to the exponential.
|
---|
| 87 | *
|
---|
| 88 | * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
|
---|
| 89 | * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
|
---|
| 90 | *
|
---|
| 91 | * \param[in] A Argument of matrix exponential
|
---|
| 92 | */
|
---|
| 93 | void pade13(const MatrixType &A);
|
---|
| 94 |
|
---|
| 95 | /** \brief Compute the (17,17)-Padé approximant to the exponential.
|
---|
| 96 | *
|
---|
| 97 | * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
|
---|
| 98 | * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
|
---|
| 99 | *
|
---|
| 100 | * This function activates only if your long double is double-double or quadruple.
|
---|
| 101 | *
|
---|
| 102 | * \param[in] A Argument of matrix exponential
|
---|
| 103 | */
|
---|
| 104 | void pade17(const MatrixType &A);
|
---|
| 105 |
|
---|
| 106 | /** \brief Compute Padé approximant to the exponential.
|
---|
| 107 | *
|
---|
| 108 | * Computes \c m_U, \c m_V and \c m_squarings such that
|
---|
| 109 | * \f$ (V+U)(V-U)^{-1} \f$ is a Padé of
|
---|
| 110 | * \f$ \exp(2^{-\mbox{squarings}}M) \f$ around \f$ M = 0 \f$. The
|
---|
| 111 | * degree of the Padé approximant and the value of
|
---|
| 112 | * squarings are chosen such that the approximation error is no
|
---|
| 113 | * more than the round-off error.
|
---|
| 114 | *
|
---|
| 115 | * The argument of this function should correspond with the (real
|
---|
| 116 | * part of) the entries of \c m_M. It is used to select the
|
---|
| 117 | * correct implementation using overloading.
|
---|
| 118 | */
|
---|
| 119 | void computeUV(double);
|
---|
| 120 |
|
---|
| 121 | /** \brief Compute Padé approximant to the exponential.
|
---|
| 122 | *
|
---|
| 123 | * \sa computeUV(double);
|
---|
| 124 | */
|
---|
| 125 | void computeUV(float);
|
---|
| 126 |
|
---|
| 127 | /** \brief Compute Padé approximant to the exponential.
|
---|
| 128 | *
|
---|
| 129 | * \sa computeUV(double);
|
---|
| 130 | */
|
---|
| 131 | void computeUV(long double);
|
---|
| 132 |
|
---|
| 133 | typedef typename internal::traits<MatrixType>::Scalar Scalar;
|
---|
| 134 | typedef typename NumTraits<Scalar>::Real RealScalar;
|
---|
| 135 | typedef typename std::complex<RealScalar> ComplexScalar;
|
---|
| 136 |
|
---|
| 137 | /** \brief Reference to matrix whose exponential is to be computed. */
|
---|
| 138 | typename internal::nested<MatrixType>::type m_M;
|
---|
| 139 |
|
---|
| 140 | /** \brief Odd-degree terms in numerator of Padé approximant. */
|
---|
| 141 | MatrixType m_U;
|
---|
| 142 |
|
---|
| 143 | /** \brief Even-degree terms in numerator of Padé approximant. */
|
---|
| 144 | MatrixType m_V;
|
---|
| 145 |
|
---|
| 146 | /** \brief Used for temporary storage. */
|
---|
| 147 | MatrixType m_tmp1;
|
---|
| 148 |
|
---|
| 149 | /** \brief Used for temporary storage. */
|
---|
| 150 | MatrixType m_tmp2;
|
---|
| 151 |
|
---|
| 152 | /** \brief Identity matrix of the same size as \c m_M. */
|
---|
| 153 | MatrixType m_Id;
|
---|
| 154 |
|
---|
| 155 | /** \brief Number of squarings required in the last step. */
|
---|
| 156 | int m_squarings;
|
---|
| 157 |
|
---|
| 158 | /** \brief L1 norm of m_M. */
|
---|
| 159 | RealScalar m_l1norm;
|
---|
| 160 | };
|
---|
| 161 |
|
---|
| 162 | template <typename MatrixType>
|
---|
| 163 | MatrixExponential<MatrixType>::MatrixExponential(const MatrixType &M) :
|
---|
| 164 | m_M(M),
|
---|
| 165 | m_U(M.rows(),M.cols()),
|
---|
| 166 | m_V(M.rows(),M.cols()),
|
---|
| 167 | m_tmp1(M.rows(),M.cols()),
|
---|
| 168 | m_tmp2(M.rows(),M.cols()),
|
---|
| 169 | m_Id(MatrixType::Identity(M.rows(), M.cols())),
|
---|
| 170 | m_squarings(0),
|
---|
| 171 | m_l1norm(M.cwiseAbs().colwise().sum().maxCoeff())
|
---|
| 172 | {
|
---|
| 173 | /* empty body */
|
---|
| 174 | }
|
---|
| 175 |
|
---|
| 176 | template <typename MatrixType>
|
---|
| 177 | template <typename ResultType>
|
---|
| 178 | void MatrixExponential<MatrixType>::compute(ResultType &result)
|
---|
| 179 | {
|
---|
| 180 | #if LDBL_MANT_DIG > 112 // rarely happens
|
---|
| 181 | if(sizeof(RealScalar) > 14) {
|
---|
| 182 | result = m_M.matrixFunction(StdStemFunctions<ComplexScalar>::exp);
|
---|
| 183 | return;
|
---|
| 184 | }
|
---|
| 185 | #endif
|
---|
| 186 | computeUV(RealScalar());
|
---|
| 187 | m_tmp1 = m_U + m_V; // numerator of Pade approximant
|
---|
| 188 | m_tmp2 = -m_U + m_V; // denominator of Pade approximant
|
---|
| 189 | result = m_tmp2.partialPivLu().solve(m_tmp1);
|
---|
| 190 | for (int i=0; i<m_squarings; i++)
|
---|
| 191 | result *= result; // undo scaling by repeated squaring
|
---|
| 192 | }
|
---|
| 193 |
|
---|
| 194 | template <typename MatrixType>
|
---|
| 195 | EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade3(const MatrixType &A)
|
---|
| 196 | {
|
---|
| 197 | const RealScalar b[] = {120., 60., 12., 1.};
|
---|
| 198 | m_tmp1.noalias() = A * A;
|
---|
| 199 | m_tmp2 = b[3]*m_tmp1 + b[1]*m_Id;
|
---|
| 200 | m_U.noalias() = A * m_tmp2;
|
---|
| 201 | m_V = b[2]*m_tmp1 + b[0]*m_Id;
|
---|
| 202 | }
|
---|
| 203 |
|
---|
| 204 | template <typename MatrixType>
|
---|
| 205 | EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade5(const MatrixType &A)
|
---|
| 206 | {
|
---|
| 207 | const RealScalar b[] = {30240., 15120., 3360., 420., 30., 1.};
|
---|
| 208 | MatrixType A2 = A * A;
|
---|
| 209 | m_tmp1.noalias() = A2 * A2;
|
---|
| 210 | m_tmp2 = b[5]*m_tmp1 + b[3]*A2 + b[1]*m_Id;
|
---|
| 211 | m_U.noalias() = A * m_tmp2;
|
---|
| 212 | m_V = b[4]*m_tmp1 + b[2]*A2 + b[0]*m_Id;
|
---|
| 213 | }
|
---|
| 214 |
|
---|
| 215 | template <typename MatrixType>
|
---|
| 216 | EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade7(const MatrixType &A)
|
---|
| 217 | {
|
---|
| 218 | const RealScalar b[] = {17297280., 8648640., 1995840., 277200., 25200., 1512., 56., 1.};
|
---|
| 219 | MatrixType A2 = A * A;
|
---|
| 220 | MatrixType A4 = A2 * A2;
|
---|
| 221 | m_tmp1.noalias() = A4 * A2;
|
---|
| 222 | m_tmp2 = b[7]*m_tmp1 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;
|
---|
| 223 | m_U.noalias() = A * m_tmp2;
|
---|
| 224 | m_V = b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;
|
---|
| 225 | }
|
---|
| 226 |
|
---|
| 227 | template <typename MatrixType>
|
---|
| 228 | EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade9(const MatrixType &A)
|
---|
| 229 | {
|
---|
| 230 | const RealScalar b[] = {17643225600., 8821612800., 2075673600., 302702400., 30270240.,
|
---|
| 231 | 2162160., 110880., 3960., 90., 1.};
|
---|
| 232 | MatrixType A2 = A * A;
|
---|
| 233 | MatrixType A4 = A2 * A2;
|
---|
| 234 | MatrixType A6 = A4 * A2;
|
---|
| 235 | m_tmp1.noalias() = A6 * A2;
|
---|
| 236 | m_tmp2 = b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;
|
---|
| 237 | m_U.noalias() = A * m_tmp2;
|
---|
| 238 | m_V = b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;
|
---|
| 239 | }
|
---|
| 240 |
|
---|
| 241 | template <typename MatrixType>
|
---|
| 242 | EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade13(const MatrixType &A)
|
---|
| 243 | {
|
---|
| 244 | const RealScalar b[] = {64764752532480000., 32382376266240000., 7771770303897600.,
|
---|
| 245 | 1187353796428800., 129060195264000., 10559470521600., 670442572800.,
|
---|
| 246 | 33522128640., 1323241920., 40840800., 960960., 16380., 182., 1.};
|
---|
| 247 | MatrixType A2 = A * A;
|
---|
| 248 | MatrixType A4 = A2 * A2;
|
---|
| 249 | m_tmp1.noalias() = A4 * A2;
|
---|
| 250 | m_V = b[13]*m_tmp1 + b[11]*A4 + b[9]*A2; // used for temporary storage
|
---|
| 251 | m_tmp2.noalias() = m_tmp1 * m_V;
|
---|
| 252 | m_tmp2 += b[7]*m_tmp1 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;
|
---|
| 253 | m_U.noalias() = A * m_tmp2;
|
---|
| 254 | m_tmp2 = b[12]*m_tmp1 + b[10]*A4 + b[8]*A2;
|
---|
| 255 | m_V.noalias() = m_tmp1 * m_tmp2;
|
---|
| 256 | m_V += b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;
|
---|
| 257 | }
|
---|
| 258 |
|
---|
| 259 | #if LDBL_MANT_DIG > 64
|
---|
| 260 | template <typename MatrixType>
|
---|
| 261 | EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade17(const MatrixType &A)
|
---|
| 262 | {
|
---|
| 263 | const RealScalar b[] = {830034394580628357120000.L, 415017197290314178560000.L,
|
---|
| 264 | 100610229646136770560000.L, 15720348382208870400000.L,
|
---|
| 265 | 1774878043152614400000.L, 153822763739893248000.L, 10608466464820224000.L,
|
---|
| 266 | 595373117923584000.L, 27563570274240000.L, 1060137318240000.L,
|
---|
| 267 | 33924394183680.L, 899510451840.L, 19554575040.L, 341863200.L, 4651200.L,
|
---|
| 268 | 46512.L, 306.L, 1.L};
|
---|
| 269 | MatrixType A2 = A * A;
|
---|
| 270 | MatrixType A4 = A2 * A2;
|
---|
| 271 | MatrixType A6 = A4 * A2;
|
---|
| 272 | m_tmp1.noalias() = A4 * A4;
|
---|
| 273 | m_V = b[17]*m_tmp1 + b[15]*A6 + b[13]*A4 + b[11]*A2; // used for temporary storage
|
---|
| 274 | m_tmp2.noalias() = m_tmp1 * m_V;
|
---|
| 275 | m_tmp2 += b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;
|
---|
| 276 | m_U.noalias() = A * m_tmp2;
|
---|
| 277 | m_tmp2 = b[16]*m_tmp1 + b[14]*A6 + b[12]*A4 + b[10]*A2;
|
---|
| 278 | m_V.noalias() = m_tmp1 * m_tmp2;
|
---|
| 279 | m_V += b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;
|
---|
| 280 | }
|
---|
| 281 | #endif
|
---|
| 282 |
|
---|
| 283 | template <typename MatrixType>
|
---|
| 284 | void MatrixExponential<MatrixType>::computeUV(float)
|
---|
| 285 | {
|
---|
| 286 | using std::frexp;
|
---|
| 287 | using std::pow;
|
---|
| 288 | if (m_l1norm < 4.258730016922831e-001) {
|
---|
| 289 | pade3(m_M);
|
---|
| 290 | } else if (m_l1norm < 1.880152677804762e+000) {
|
---|
| 291 | pade5(m_M);
|
---|
| 292 | } else {
|
---|
| 293 | const float maxnorm = 3.925724783138660f;
|
---|
| 294 | frexp(m_l1norm / maxnorm, &m_squarings);
|
---|
| 295 | if (m_squarings < 0) m_squarings = 0;
|
---|
| 296 | MatrixType A = m_M / Scalar(pow(2, m_squarings));
|
---|
| 297 | pade7(A);
|
---|
| 298 | }
|
---|
| 299 | }
|
---|
| 300 |
|
---|
| 301 | template <typename MatrixType>
|
---|
| 302 | void MatrixExponential<MatrixType>::computeUV(double)
|
---|
| 303 | {
|
---|
| 304 | using std::frexp;
|
---|
| 305 | using std::pow;
|
---|
| 306 | if (m_l1norm < 1.495585217958292e-002) {
|
---|
| 307 | pade3(m_M);
|
---|
| 308 | } else if (m_l1norm < 2.539398330063230e-001) {
|
---|
| 309 | pade5(m_M);
|
---|
| 310 | } else if (m_l1norm < 9.504178996162932e-001) {
|
---|
| 311 | pade7(m_M);
|
---|
| 312 | } else if (m_l1norm < 2.097847961257068e+000) {
|
---|
| 313 | pade9(m_M);
|
---|
| 314 | } else {
|
---|
| 315 | const double maxnorm = 5.371920351148152;
|
---|
| 316 | frexp(m_l1norm / maxnorm, &m_squarings);
|
---|
| 317 | if (m_squarings < 0) m_squarings = 0;
|
---|
| 318 | MatrixType A = m_M / Scalar(pow(2, m_squarings));
|
---|
| 319 | pade13(A);
|
---|
| 320 | }
|
---|
| 321 | }
|
---|
| 322 |
|
---|
| 323 | template <typename MatrixType>
|
---|
| 324 | void MatrixExponential<MatrixType>::computeUV(long double)
|
---|
| 325 | {
|
---|
| 326 | using std::frexp;
|
---|
| 327 | using std::pow;
|
---|
| 328 | #if LDBL_MANT_DIG == 53 // double precision
|
---|
| 329 | computeUV(double());
|
---|
| 330 | #elif LDBL_MANT_DIG <= 64 // extended precision
|
---|
| 331 | if (m_l1norm < 4.1968497232266989671e-003L) {
|
---|
| 332 | pade3(m_M);
|
---|
| 333 | } else if (m_l1norm < 1.1848116734693823091e-001L) {
|
---|
| 334 | pade5(m_M);
|
---|
| 335 | } else if (m_l1norm < 5.5170388480686700274e-001L) {
|
---|
| 336 | pade7(m_M);
|
---|
| 337 | } else if (m_l1norm < 1.3759868875587845383e+000L) {
|
---|
| 338 | pade9(m_M);
|
---|
| 339 | } else {
|
---|
| 340 | const long double maxnorm = 4.0246098906697353063L;
|
---|
| 341 | frexp(m_l1norm / maxnorm, &m_squarings);
|
---|
| 342 | if (m_squarings < 0) m_squarings = 0;
|
---|
| 343 | MatrixType A = m_M / Scalar(pow(2, m_squarings));
|
---|
| 344 | pade13(A);
|
---|
| 345 | }
|
---|
| 346 | #elif LDBL_MANT_DIG <= 106 // double-double
|
---|
| 347 | if (m_l1norm < 3.2787892205607026992947488108213e-005L) {
|
---|
| 348 | pade3(m_M);
|
---|
| 349 | } else if (m_l1norm < 6.4467025060072760084130906076332e-003L) {
|
---|
| 350 | pade5(m_M);
|
---|
| 351 | } else if (m_l1norm < 6.8988028496595374751374122881143e-002L) {
|
---|
| 352 | pade7(m_M);
|
---|
| 353 | } else if (m_l1norm < 2.7339737518502231741495857201670e-001L) {
|
---|
| 354 | pade9(m_M);
|
---|
| 355 | } else if (m_l1norm < 1.3203382096514474905666448850278e+000L) {
|
---|
| 356 | pade13(m_M);
|
---|
| 357 | } else {
|
---|
| 358 | const long double maxnorm = 3.2579440895405400856599663723517L;
|
---|
| 359 | frexp(m_l1norm / maxnorm, &m_squarings);
|
---|
| 360 | if (m_squarings < 0) m_squarings = 0;
|
---|
| 361 | MatrixType A = m_M / pow(Scalar(2), m_squarings);
|
---|
| 362 | pade17(A);
|
---|
| 363 | }
|
---|
| 364 | #elif LDBL_MANT_DIG <= 112 // quadruple precison
|
---|
| 365 | if (m_l1norm < 1.639394610288918690547467954466970e-005L) {
|
---|
| 366 | pade3(m_M);
|
---|
| 367 | } else if (m_l1norm < 4.253237712165275566025884344433009e-003L) {
|
---|
| 368 | pade5(m_M);
|
---|
| 369 | } else if (m_l1norm < 5.125804063165764409885122032933142e-002L) {
|
---|
| 370 | pade7(m_M);
|
---|
| 371 | } else if (m_l1norm < 2.170000765161155195453205651889853e-001L) {
|
---|
| 372 | pade9(m_M);
|
---|
| 373 | } else if (m_l1norm < 1.125358383453143065081397882891878e+000L) {
|
---|
| 374 | pade13(m_M);
|
---|
| 375 | } else {
|
---|
| 376 | const long double maxnorm = 2.884233277829519311757165057717815L;
|
---|
| 377 | frexp(m_l1norm / maxnorm, &m_squarings);
|
---|
| 378 | if (m_squarings < 0) m_squarings = 0;
|
---|
| 379 | MatrixType A = m_M / Scalar(pow(2, m_squarings));
|
---|
| 380 | pade17(A);
|
---|
| 381 | }
|
---|
| 382 | #else
|
---|
| 383 | // this case should be handled in compute()
|
---|
| 384 | eigen_assert(false && "Bug in MatrixExponential");
|
---|
| 385 | #endif // LDBL_MANT_DIG
|
---|
| 386 | }
|
---|
| 387 |
|
---|
| 388 | /** \ingroup MatrixFunctions_Module
|
---|
| 389 | *
|
---|
| 390 | * \brief Proxy for the matrix exponential of some matrix (expression).
|
---|
| 391 | *
|
---|
| 392 | * \tparam Derived Type of the argument to the matrix exponential.
|
---|
| 393 | *
|
---|
| 394 | * This class holds the argument to the matrix exponential until it
|
---|
| 395 | * is assigned or evaluated for some other reason (so the argument
|
---|
| 396 | * should not be changed in the meantime). It is the return type of
|
---|
| 397 | * MatrixBase::exp() and most of the time this is the only way it is
|
---|
| 398 | * used.
|
---|
| 399 | */
|
---|
| 400 | template<typename Derived> struct MatrixExponentialReturnValue
|
---|
| 401 | : public ReturnByValue<MatrixExponentialReturnValue<Derived> >
|
---|
| 402 | {
|
---|
| 403 | typedef typename Derived::Index Index;
|
---|
| 404 | public:
|
---|
| 405 | /** \brief Constructor.
|
---|
| 406 | *
|
---|
| 407 | * \param[in] src %Matrix (expression) forming the argument of the
|
---|
| 408 | * matrix exponential.
|
---|
| 409 | */
|
---|
| 410 | MatrixExponentialReturnValue(const Derived& src) : m_src(src) { }
|
---|
| 411 |
|
---|
| 412 | /** \brief Compute the matrix exponential.
|
---|
| 413 | *
|
---|
| 414 | * \param[out] result the matrix exponential of \p src in the
|
---|
| 415 | * constructor.
|
---|
| 416 | */
|
---|
| 417 | template <typename ResultType>
|
---|
| 418 | inline void evalTo(ResultType& result) const
|
---|
| 419 | {
|
---|
| 420 | const typename Derived::PlainObject srcEvaluated = m_src.eval();
|
---|
| 421 | MatrixExponential<typename Derived::PlainObject> me(srcEvaluated);
|
---|
| 422 | me.compute(result);
|
---|
| 423 | }
|
---|
| 424 |
|
---|
| 425 | Index rows() const { return m_src.rows(); }
|
---|
| 426 | Index cols() const { return m_src.cols(); }
|
---|
| 427 |
|
---|
| 428 | protected:
|
---|
| 429 | const Derived& m_src;
|
---|
| 430 | private:
|
---|
| 431 | MatrixExponentialReturnValue& operator=(const MatrixExponentialReturnValue&);
|
---|
| 432 | };
|
---|
| 433 |
|
---|
| 434 | namespace internal {
|
---|
| 435 | template<typename Derived>
|
---|
| 436 | struct traits<MatrixExponentialReturnValue<Derived> >
|
---|
| 437 | {
|
---|
| 438 | typedef typename Derived::PlainObject ReturnType;
|
---|
| 439 | };
|
---|
| 440 | }
|
---|
| 441 |
|
---|
| 442 | template <typename Derived>
|
---|
| 443 | const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const
|
---|
| 444 | {
|
---|
| 445 | eigen_assert(rows() == cols());
|
---|
| 446 | return MatrixExponentialReturnValue<Derived>(derived());
|
---|
| 447 | }
|
---|
| 448 |
|
---|
| 449 | } // end namespace Eigen
|
---|
| 450 |
|
---|
| 451 | #endif // EIGEN_MATRIX_EXPONENTIAL
|
---|